Local Moment Formation by Vacancies in Mono-layer Graphene

TL;DR

This paper investigates how vacancies in monolayer graphene induce localized magnetic moments, focusing on the effects of hopping parameters and the resulting electronic states, revealing conditions for local moment formation and potential high-temperature magnetism.

Contribution

It introduces a Green's function approach to analyze vacancy-induced magnetic moments in graphene, emphasizing the role of second neighbor hopping and topological localization effects.

Findings

Vacancy-induced zero-mode states are sublattice-dependent and affected by hopping ratios.

Local magnetic moments form due to Hund's coupling with nearby sigma states.

Potential for high Curie temperatures due to poor screening of vacancy moments.

Abstract

We employ the Green's function technique to investigate the vacancy-induced quasi-localized magnetic moment formation in mono-layer graphene starting with the Dirac Hamiltonian, which focuses on the {\pi}- orbitals only, involving the nearest neighbor(NN)(t) and moderate second neighbor(SN)(t' < t/3) hopping integrals. The vacancy defect is modeled by the addition of the on-site perturbation potential to the Hamiltonian. We find that, when (t'/t) << 1, the vacancy induced {\pi}-state at the zero of energy(zero-mode state(ZMS)) does not inhabit the minority sub-lattice due to the strong scalar potential induced by the vacancy(the ZMSs get lodged in the majority sub-lattice) whereas, when (t'/t) is increased, the ZMS is somewhat suppressed. This shows that, not only the shift of the Fermi energy away from the linearly-dispersive Dirac points, the issue of this topological localization is also hinged on the ratio (t'/t). Furthermore, when a vacancy is present, the three sp2- hybridized {\sigma} states of each of the three nearest-neighbor carbon atoms, forming a carbon triangle surrounding the vacancy, are close to the Fermi energy (EF). The Hund's coupling between these {\sigma} electrons and the remaining electron which occupies the {\pi} state spin polarizes the {\pi} state leading to local moment formation close to EF. Since the system at the Fermi level has low electronic density, there is poor screening of such magnetic moments. This may lead to a high Curie temperature for such vacancy-induced moments.